Rapidly tunable, narrow-band infrared filter arrays

ABSTRACT

Tunable filters can use Fano metasurface designs having extremely narrow transmission bands. The Fano metasurface can comprise dielectric or semiconductor materials and can produce transmission bands with quality factors well in excess of 1000—at least a factor of 50 greater than typical metamaterial-based infrared resonances. Numerical simulations of these metasurfaces show that the spectral position of the passband can be changed by slightly changing the position of a small dielectric perturbation block placed within the near-field of the resonator by using simple electromechanical actuation architectures that allow for such motion. An array of independently tunable narrowband infrared filters can thereby be fabricated that only requires deep-subwavelength motions of perturbing objects in the resonator&#39;s near-field.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of U.S. application Ser. No.15/227,440, filed Aug. 3, 2016, which claims the benefit of U.S.Provisional Application No. 62/212,258, filed Aug. 31, 2015, both ofwhich are incorporated herein by reference.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with Government support under Contract No.DE-NA0003525 awarded by the United States Department of Energy/NationalNuclear Security Administration. The Government has certain rights inthe invention.

FIELD OF THE INVENTION

The present invention relates to infrared filter arrays and, inparticular, to a rapidly tunable, narrow-band infrared filter arraybased on a Fano metasurface.

BACKGROUND OF THE INVENTION

Metasurfaces are the two-dimensional surface counterparts of the fullythree-dimensional bulk metamaterials. Metasurfaces are currently thesubject of intensive research worldwide since they can be tailored toproduce a wide range of optical behaviors. However, metasurfacesgenerally exhibit broad spectral resonances, and it is difficult toobtain narrow (i.e. high quality-factor, Q) spectral features. Attainingsuch high-Q features from metasurfaces would greatly expand theirapplication space, particularly in the areas of sensing, spectralfiltering, and optical modulation. Early metasurfaces were fabricatedfrom metals and exhibited particularly broad resonances at infrared andoptical frequencies as a result of Ohmic losses. Dielectricresonator-based metasurfaces were introduced to overcome these lossesand have enabled, among others, wave-front manipulation and cloakingdevices, perfect reflectors, and ultrathin lenses but, althoughabsorptive losses were reduced, the metasurface resonances remainedbroad due to strong coupling with the external field (i.e. largeradiation losses). See J. C. Ginn et al., Phys. Rev. Lett. 108 (9),097402 (2012); I. Staude et al., ACS Nano 7 (9), 7824 (2013); A. Arbabiet al., Nat. Nano 10 (11), 937 (2015); S. Jahani and Z. Jacob, Nat. Nano11 (1), 23 (2016); M. I. Shalaev et al., Nano Lett. 15 (9), 6261 (2015);K. E. Chong et al., Nano Lett. 15 (8), 5369 (2015); D. Lin et al.,Science 345 (6194), 298 (2014); L. Y. Hsu et al., Prog. Electromagn.Res. 152, 33 (2015); P. R. West et al., Opt. Express 22 (21), 26212(2014); and P. Moitra et al., ACS Photonics 2 (6), 692 (2015).

Recently, new strategies based on “electromagnetically inducedtransparency” or “Fano resonances” have been developed that show greatpromise for achieving high-Q resonances. See C. Wu et al., Nat. Mater.11 (1), 69 (2012); R. Singh et al., Appl. Phys. Lett. 105 (17), 171101(2014); C. Wu et al., Nat. Commun. 5, (2014); Y. Yang et al., Nat.Commun. 5, (2014); and W. Zhao et al., Opt. Express 23 (5), 6858 (2015).In this approach, the resonator system is designed to support both“bright” and “dark” resonances. The incident optical field readilycouples to the bright resonance, but cannot couple directly to the darkresonance. Through proper design, a weak coupling between the tworesonances can be introduced, allowing energy from the incident wave tobe indirectly coupled to the dark resonance. The metasurfacetransmission and reflection spectra resulting from such an approachfeature Fano resonances that can be much narrower than the traditionalmetasurface resonances. This approach has been demonstrated formetal-based metasurfaces at THz frequencies where Q-factors approaching100 have been observed. See C. Wu et al., Nat. Mater. 11 (1), 69 (2012);and R. Singh et al., Appl. Phys. Lett. 105 (17), 171101 (2014).

Even more dramatic results have been achieved by applying this strategyto dielectric resonator-based metasurfaces and Q-factors approaching 500have been demonstrated. See Y. Yang et al., Nat. Commun. 5, (2014). Acommon feature of the dielectric resonator-based Fano designsdemonstrated thus far is the reliance on multiple, distinct, near-fieldcoupled dielectric structures within the unit cell. See Y. Yang et al.,Nat. Commun. 5, (2014); W. Zhao et al., Opt. Express 23 (5), 6858(2015); and F. Wang et al., Opt. Mater. Express 5 (3), 668 (2015).However, reliable and repeatable control of near-field coupling requiresexacting fabrication tolerances.

Further, a need remains for a rapidly tunable, narrowband filter arraythat can be integrated with infrared (IR) focal plane arrays for a widerange of imaging and sensing applications. Current state-of-the-art fortunable focal plane filter arrays relies on microelectromechanicalsystems (MEMS)-based Fabry-Perot filters which produce spectrally broadtransmission pass bands. See W. J. Gunning et al., Proc. SPIE 5783, 366(2005). Furthermore, the tunable Fabry-Perot infrared filter arrayrequires MEMS-based motion over large distances (of order thewavelength) to tune the spectral passband. Other approaches includeliquid crystal devices, which are slow, lossy, and don't achieve narrowpassbands; phase change materials such as VO₂, which are notcontinuously tunable and do not produce desirable passband spectralprofiles; and metasurface arrays fabricated on stretchable membranes,which rely on the impractical tuning mechanism of stretching. See H.Zhang et al., Appl. Opt. 53, 5632 (2014); H. Kocer et al., Appl. Phys.Lett. 106, 161104 (2015), and I. M. Pryce et al., Nano Lett.10, 4222(2010).

SUMMARY OF THE INVENTION

The present invention is directed to a rapidly tunable, narrow-bandfilter array that can be integrated with IR focal plane arrays. Thetunable filter is based on a new, monolithic all-dielectric resonatormetasurface that yields high quality-factor Fano resonances. Theinvention utilizes perturbations of high-symmetry resonator structuresto induce couplings between the otherwise orthogonal resonator modes. Inparticular, the perturbations couple “bright” dipole modes to “dark”dipole modes whose emission is suppressed by local field effects.Numerical simulations of these Fano metasurfaces show that the spectralposition of the passband can be changed by slightly changing theposition of a small dielectric perturbation, such as a block, placedwithin the near-field of the resonator. Therefore, these metasurfacescan be made with spectral tunability by using simple electromechanicalactuation architectures that allow for such motion. In particular,deep-subwavelength motions of dielectric blocks in the resonator'snear-field can provide an array of independently tunable narrowbandinfrared filters. This device is superior to the Fabry-Perot approachbecause it requires significantly less MEMS-based motion and can achievesignificantly narrower transmission linewidths. For example, simulationsof a Fano metasurface-based tunable filter array operating in thethermal infrared (8-12 μm) show that Fano resonance can shift by manymultiples of its linewidth. These infrared filter arrays can be coupledwith infrared focal plane arrays to enable a wide range of infraredimaging and sensing capabilities.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description will refer to the following drawings, whereinlike elements are referred to by like numbers.

FIGS. 1A and 1 b are schematic illustrations depicting the operatingprinciples of the Fano metasurfaces. FIG. 1A shows that the electricfield of the incident radiation excites only the p_(x) electric dipolemode of the cube resonators (dark arrows). The decay of the electricdipole mode is governed by both radiative (r) and non-radiative (nr)processes. FIG. 1B shows how symmetry breaking can be used to allowcoupling of the p_(x) dipole to the longitudinal m_(z) magnetic dipole(dark loops) which only decays due to non-radiative losses (neglectingthe small coupling to radiating moments). A similar process (not shown)involving the bright in-plane magnetic dipole (m_(y)) and darklongitudinal electric dipole (p_(z)) leads to a second Fano resonance athigher energy.

FIG. 2 is a perspective view schematic illustration of the unit cell ofa germanium Fano metasurface design. The period of the metasurface is4.2 μm.

FIG. 3 is the reflectivity spectrum of the array in FIG. 2 obtainedusing full-wave simulations. The inset on the left shows an expandedview of the resonance at ˜10.8 μm. The Q-factor for this resonance is˜1300. The inset on the right shows a vector plot of the electric fieldin the x-y resonator mid-plane featuring a circulating pattern.

FIG. 4 is a graph of the power radiated by the four dominant multipolesof the Fano resonators when excited in the array (no substrate). At theresonant frequency the x-directed electric dipole is largelyextinguished and the z-directed magnetic dipole dominates.

FIG. 5 is a graph of the absolute magnitude of the magnetic fieldenhancement for the centermost resonator as a function of array size.The enhancement rises sharply with array size for the smaller arrays,and is beginning to saturate at the largest (9×9) array. The overallsize of the array required to achieve a robust Fano resonance is quitesmall.

FIG. 6 is a perspective view schematic illustration of an exemplarysilicon-on-insulator resonator array Fano metasurface. The period of themetasurface is 550 nm.

FIG. 7 is the experimentally measured reflectivity spectrum of the Siresonator array shown in the inset. The Q-factor for the resonance at998.8 nm is ˜350.

FIG. 8 is a perspective view schematic illustration of an exemplaryGaAs-based Fano metasurface.

FIG. 9 is a graph of the measured reflectivity spectrum from threeGaAs-based Fano metasurfaces with slightly different in-plane scalings(s) of a nominal 270×270×300 nm³ design. The array corresponding to thelargest scaling factor exhibits a resonance with a FWHM of 1.6 nm,corresponding to a Q-factor of approximately 600. The inset shows an SEMof several of the resonators in the s=0.95 array.

FIG. 10A is a schematic illustration of normal tuning of a Fanometasurface-based tunable filter array. The Fano transmission resonanceshifts as the perturbing block moves in a direction normal to theresonator face. FIG. 10B is a schematic illustration of lateral tuning.Moving the perturbing block laterally from a high symmetry positioncauses the Fano transmission resonance to appear. The spectral positionof the resonance depends on the magnitude of the lateral shift.

FIGS. 11A and 11B are schematic Illustrations of MEMS-like actuation forvertical tuning the Fano resonances of an array. FIG. 11A shows theperturbing blocks in a near-field position. FIG. 11B shows verticaltuning by collectively moving all the perturbing blocks downward fromthe cubic resonators.

FIGS. 12A and 12B are schematic Illustrations of MEMS-like actuation forlateral tuning the Fano resonances of an array. FIG. 12A shows theperturbing blocks in a near-field position. FIG. 12B shows lateraltuning by collectively moving all the perturbing blocks laterally withrespect to the cubic resonators.

FIGS. 13A and 13B are schematic illustrations of a vertically tuned Fanometasurface. FIG. 13A shows the perturbing block initially in the nearfield of the dielectric resonator. FIG. 13B shows the perturbing blockin a position that destroys the asymmetry of the resonator, and hencethe Fano resonance.

DETAILED DESCRIPTION OF THE INVENTION

Dielectric resonators are generally fabricated from high permittivitymaterials, such as Te, Ge, GaAs, Si, or PbTe, so that the dimensions ofthe resonator are smaller than the free-space wavelength at theresonator's resonant frequencies (as used herein, “dielectric” caninclude both insulating and semiconducting materials). Dielectricresonators are generally fabricated using symmetric geometries such ascubes or spheres. However, a symmetric geometry is not required providedthe resonator supports an in-plane dipole mode (electric or magnetic)that can couple to incoming and outgoing plane waves. The resonant modesof symmetric resonators are orthogonal and do not couple to each other.However, certain classes of perturbations to the resonator geometry caninduce coupling between the otherwise orthogonal modes. For example, oneof a cubic resonator's side walls can be tilted (either in-plane orout-of-plane), or a notch can be cut near one edge of the resonator.Other geometric perturbations are possible. In addition, theperturbation can utilize other dielectric materials that are distinctfrom the material from which the resonator is fabricated. For example,the “notch” cut from the edge of the resonator can be filled with adifferent material with a larger or smaller permittivity than that ofthe dielectric resonator structure. The perturbation can also comprisean anisotropic material coupling to the out-of-plane moments. Whenperturbed in this manner, the in-plane and out-of-plane modes largelyretain their character (i.e. the z-directed magnetic dipole of thesymmetric resonator still has the character of a z-directed magneticdipole in the perturbed resonator).

Dielectric resonator metasurfaces are two-dimensional, periodic arraysof dielectric resonators. The metasurfaces are non-diffractive when theperiod of the array is smaller than the free-space wavelength. In thiscase the arrays can be optically characterized by their transmission andreflection spectra. For symmetric resonators, the metasurfaces willexhibit broad spectral regions of high reflectivity at the electric andmagnetic dipole resonances. However, metasurfaces of properly perturbedresonators will feature extremely sharp spectral transmission resonancesin addition to the broad reflection peaks.

This new metasurface design relies on a single resonator per unit celland produces robust, high quality-factor Fano resonances. Themetasurface utilizes symmetry breaking of highly symmetric resonatorgeometries, such as a cube, sphere, prism, pyramid, or cylinder, toinduce couplings between the otherwise orthogonal resonator modes. Inparticular, the perturbations couple “bright” dipole modes to “dark”dipole modes whose radiative decay is suppressed by local field effectsin the array. The design is widely scalable from the near-infrared toradio frequencies (e.g., 0.75 μm to 1 m wavelength). The resonator cancomprise a high permittivity or high refractive index material (thepermittivity, ε, and refractive index, n, are related by ε=n² innon-magnetic materials), such as Te, Ge, Si, or a IV-VI compoundcomprising lead, such as PbTe. Alternatively, the resonator can comprisea III-V compound having a high refractive index, such as GaAs, GaN, orother III-V alloys. An array of such resonators can be fabricated on alow-loss substrate having a lower refractive index than the resonatormaterial. For example, both silicon dioxide and barium fluoride have arefractive index of about 1.45 in the near-infrared. When thesematerials are used as a substrate, the refractive index of the resonatorshould be greater than about 2.5. For example, the resonator cancomprise Si or GaAs which have refractive indices of about 3.5 in thenear-infrared. If a high index substrate is used, the substrate canfurther comprise an intermediate layer having a low refractive indexthat can be used to separate the high index dielectric resonator fromthe high index substrate so that the mode is still confined within theresonator.

As described below, Fano resonance behavior is demonstrated throughnumerical simulations of a germanium resonator-based metasurface thatachieves a quality-factor of ˜1300 at ˜10.8 μm. As examples, twometasurfaces were fabricated that operate in the near-infrared (˜1 μm):a silicon-based metasurface that achieves a quality-factor of ˜350; anda gallium arsenide-based metasurface that achieves a quality-factor of˜600. In both examples, large electromagnetic field enhancements appearwithin the resonators at the Fano resonant frequencies. Combining highquality-factor, high field enhancement resonances with nonlinear andactive/gain materials, such as gallium arsenide, can provide new classesof active optical devices.

The principles underlying the high-Q Fano metasurface are shownschematically in FIGS. 1A and 1B. An exemplary resonator design startswith a simple cubic resonator similar to the dielectric resonatorsdemonstrated in J. C. Ginn et al. See J. C. Ginn et al., Phys. Rev.Lett. 108 (9), 097402 (2012). For an isolated resonator, such ahigh-symmetry geometry leads to orthogonal, but degenerate, sets ofelectric and magnetic dipole modes oriented along the x-, y- andz-directions (along with other higher order multipoles). When arrangedin an array with subwavelength periodicity, only the transverse (i.e.in-plane) dipole modes can couple to a normally incident electromagneticwave, as shown in FIG. 1A, and this results in the usual (broad)electric and magnetic transmission/reflection resonances. See J. C. Ginnet al., Phys. Rev. Lett. 108 (9), 097402 (2012), which is incorporatedherein by reference. However, it is possible to “perturb” the geometryto change the spectral positions of the modes, or even to induce modemixing between the transverse and longitudinal dipole modes. See L. K.Warne et al., Prog. Electromagn. Res. B 44, 1 (2012); L. K. Warne etal., IEEE Trans. Antennas Propagat. 61 (4), 2130 (2013); S. Campione etal., Opt. Express 23 (3), 2293 (2015); and U.S. Pat. No. 9,374,887, eachof which is incorporated herein by reference. FIG. 1B shows a symmetrybreaking induced coupling between the p_(x) electric dipole mode and thelongitudinal m_(z) magnetic dipole mode. While the p_(x) dipole issubject to both radiative and non-radiative decay processes, the m_(z)mode is subject to only non-radiative decay and high Q-values can beachieved using low-loss dielectric materials. The interference betweenthese two modes leads to the observed high-Q Fano resonances. A similarprocess (not shown) involving the bright in-plane magnetic dipole(m_(y)) and dark longitudinal electric dipole (p_(z)) leads to a secondFano resonance at higher energy.

FIG. 2 is a schematic illustration of such a broken symmetry resonatordesign that utilizes germanium as the resonator material. Starting witha cubic geometry of nominal side length 2.53 μm, a small notch is cutfrom one corner of the cube and the adjacent corner has been slightlyextended. The resonators are arrayed on a barium fluoride (BaF₂)substrate with an array period of 4.2 μm. Such a low index substrate isnecessary to retain the original Mie modes of the dielectric resonators.See J. C. Ginn et al., Phys. Rev. Lett. 108 (9), 097402 (2012).

FIG. 3 shows the reflectivity spectrum of the germanium resonator arrayunder x-polarized incidence obtained from a Finite Difference TimeDomain (FDTD) simulation. Several extremely narrow Fano resonances areobserved—the transmission spectrum (not shown) exhibits complementary(pass-band) transmission resonances. Note that the Ge properties used inthe simulations included the appropriate material absorptive lossvalues. The quality-factor of the Fano reflection resonance (as definedby λ₀/Δλ where λ₀ is the resonant frequency and Δλ, is the full width athalf minimum (FWHM) of the resonance) at ˜10.8 μm exceeds 1300.Furthermore, at the Fano resonant frequency, the electric and magneticfields within the resonator are enhanced by several orders of magnituderelative to the incident field (not shown here).

The inset of FIG. 3 shows a vector plot of the electric field in the x-yplane located half way through the resonator and calculated at the Fanoresonance at 10.8 μm. The circulating electric field seen in the insetis reminiscent of a magnetic dipole field pattern; however, rather thanthe usual in-plane magnetic dipole, the orientation of the resonantdipole is out of the plane of the array (i.e. a z-directed magneticdipole). To further confirm this assignment, the following “numericalexperiment” was performed. First, the on-resonance response of the arraywas simulated (without a substrate for simplicity), placing a fictitiousbox around the center resonator of the array. Using Love's EquivalencePrinciple, the sources within the box (i.e. the central resonator) werereplaced with equivalent electric and magnetic surface currents derivedfrom the total tangential fields on the box. All the other resonators inthe array were removed and the fields radiated by the surface currentson the box were calculated. The radiated far-fields were then decomposedinto their multipole components including all the quadrupolecontributions. See S. Campione et al., Opt. Express 23 (3), 2293 (2015).FIG. 4 shows the power radiated by the dominant four multipoles (thepowers of the multipole components not shown in the figure are severalorders of magnitude smaller than the dominant multipoles). Above andbelow the resonant frequency of ˜27.8 THz (˜10.8 μm), the x-directedelectric dipole (p_(x)) dominates, as expected. However, in the vicinityof the Fano resonance the strength of p_(x) decreases dramatically.Simultaneously, the strength of the z-directed magnetic dipole (m_(z))increases remarkably and dominates all other multipoles by nearly twoorders of magnitude. This excitation occurs indirectly, through couplingto the x-directed electric dipole. This confirms the earlier assignmentof the resonant mode as m_(z). Note also that at the resonant frequencythe y-directed electric dipole (p_(y)) and the z-x magnetic quadrupole(M_(zx)) are also excited. However, the fields radiated by p_(y) andM_(zx) largely cancel each other in the forward and backward directions,which, in combination with the dramatic decrease of p_(x), explains thehigh transmission and low reflection observed at the Fano resonance. Thelack of perfect cancellation between p_(y) and M_(zx) results in a smalldepolarization of the transmitted wave. The reflection spectrum shown inFIG. 3 exhibits an additional Fano resonance at shorter wavelengths. Asimilar analysis shows that the origin of the higher energy Fanoresonance appearing at ˜9.7 μm in this figure is analogous to themechanism described above. However, in this case the bright mode is anin-plane magnetic dipole (m_(y)) and the dark mode is a longitudinalelectric dipole (p_(z)).

The excitation of the m_(z) multipole likely arises due to the differentwidths (in the x-direction) of the two parts of the resonator.Considering each part of the resonator as a separate polarizabledielectric region, it can be seen that such an approximate spatialdecomposition indicates the two separated electric dipoles will exhibitslightly different dipole strengths. Upon excitation with an x-polarizedwave, the asymmetry of the two dipoles will lead to a z-directedmagnetic field in the vicinity of the center of the resonator which cancouple to and excite the m_(z) dipole. Such an excitation mechanism isunavailable for the symmetric full cube resonator.

The large Q-factors of the Fano resonances arise due to the smallradiative and non-radiative decay rates of the z-directed magneticdipole in the array. For an isolated resonator, the z-directed dipole isfree to radiate and is also subject to non-radiative decay processesarising from material absorption. This results in broad resonancelinewidths for the isolated resonator. In contrast, when placed in thetwo-dimensional array, the resonator's normal radiative decay iscompensated by driving terms arising from the local field at theposition of the resonator, leaving only the (small) non-radiativeprocesses. See S. Tretyakov, Analytical Modeling in AppliedElectromagnetics, London, UK: Artech House (2003); and J. E. Sipe and J.V. Kranendonk, Phys. Rev. A 9 (5), 1806 (1974). Thus, the overallQ-factor of the resonators, and hence the Q-factor of the Fanoresonance, becomes large. To demonstrate the importance of array effectsin establishing the Fano resonance, the response of finite sized arrays(no substrate for simplicity) of varying sizes was simulated. For theisolated resonator, no Fano resonance is observed and the electric fieldvector plots are reminiscent of a p_(x) excitation. For the othersimulations, the frequency of the Fano resonance shifts slightly as thearray size increases. The 3×3 array shows a very weak Fano resonance,and the on-resonance electric field vector plots are complicated butbegin to show field circulation within each resonator. The 5×5 arrayexhibits a clear Fano resonance, and the vector field plots for theinterior resonators clearly show the electric field circulationassociated with the m_(z) dipole. Interestingly, the innermost resonatorof the array shows the largest field enhancement, while the resonatorsat the edge of the array (which experience a drastically different localfield and can radiate substantially more) show smaller fieldenhancements and less well defined modes. Proceeding to the 7×7 and 9×9arrays, the number of interior resonators experiencing large fieldenhancements increases with array size, and once again the outermostresonators show weaker excitations. The absolute magnitude of the fieldenhancement for the centermost resonator rises sharply with array sizefor the smaller arrays, and is beginning to saturate at the largest(9×9) array, as shown in FIG. 5. Thus, the overall size of the arrayrequired to achieve a robust Fano resonance is quite small.

As an example of the invention, a silicon-based Fano metasurfaceoperating near 1 μm wavelength was designed and fabricated, as shown inFIG. 6. The resonators were fabricated using silicon-on-insulator waferswith a 250 nm thick silicon layer. The nominal side length of theresonators was 280 nm and the array spacing was 550 nm. The arrays werefabricated using e-beam lithography and reactive ion etching.Reflectivity spectra were measured using a custom built near-infraredpolarizing microscope coupled to a high-resolution spectrometer equippedwith a CCD array detector. The inset of FIG. 7 shows a scanning electronmicrograph (SEM) of several of the resonators in the array, along withthe experimentally measured reflectivity spectrum. The measured spectrumshown in FIG. 7 is very similar to the simulated spectrum (not shown),although an overall wavelength shift is observed. This shift isattributed to slight dimensional differences between the designed andfabricated arrays. The measured quality-factor of the resonance at 998.8nm is about 350. There is also a slight difference between the simulatedand measured spectra in the shape of the shorter wavelength Fanoresonance that is likely due to a small inaccuracy in the SOI buriedoxide thickness used in the simulations. The buried oxide forms a lowfinesse etalon that interferes with the Fano behavior and modulates theoverall shape of the resonance.

For another example of the broken symmetry Fano approach, a GaAs-basedFano metasurface was fabricated by adapting a processing schemeoriginally developed for surface emitting semiconductor lasers. See K.D. Choquette et al., IEEE J. Sel. Topics Quantum Electron. 3 (3), 916(1997); and K. D. Choquette et al., IEEE Photon. Technol. Lett. 7 (11),1237 (1995). In contrast to indirect bandgap Si used in the experimentaldemonstration described above, GaAs features a direct bandgap so thatresidual absorptive losses should be smaller in the near-infraredspectral range and larger Q-values might be possible. The resonatorarrays were fabricated using epitaxially-grown GaAs layers and employ anovel means of isolating the resonators from the native GaAs substrateon which they were grown with a resonator-shaped AlGaO intermediatelayer (alternatively, a continuous AlGaO intermediate layer could beused). Three GaAs Fano resonators with the same array pitch of 470 nmand height of 300 nm but different in-plane unit cell dimensionalscaling factors of s=0.89, 0.92, and 0.95. FIG. 8 shows a schematic ofthe unit cell with a scaling factor of 1 that comprises a cuboid withnominal side length of 270 nm and a smaller cuboid notch with sidedimensions of x=70 nm and y=190 nm cutting through the resonator.

FIG. 9 shows the experimental reflectivity spectrum for three GaAs Fanometasurfaces with slightly different in-plane dimensional scalingfactors, s, of a nominal 270×270×300 nm³ (s=1.0) design. As expected,the Fano resonances shift to longer wavelength as the scaling factorincreases. Notably, the FWHM of the Fano resonance is 1.6 nm for themetasurface corresponding to the largest scaling factor. Thiscorresponds to a Q-factor of ˜600. Low temperature reflectivitymeasurements (not shown here) showed a shifting of the spectral locationof the Fano resonance, but did not reveal any further narrowing of theresonance. The achievement of such high-Q resonances along with theirlarge field enhancements in GaAs is particularly exciting since it opensup new avenues for device designs that exploit the active and nonlinearproperties of GaAs.

Tunable, Narrowband Filter Array

Tunable filters can use the Fano metasurface designs having extremelynarrow transmission bands. As described above, the Fano metasurface cancomprise dielectric or semiconductor materials, such as Si, GaAs, andGe, and can produce transmission bands with quality factors well inexcess of 1000—at least a factor of 50 greater than typicalmetamaterial-based IR resonances. Numerical simulations of thesemetasurfaces show that the spectral position of the passband can bechanged by slightly changing the position of a small dielectricperturbation block placed within the near-field of the resonator. Thesemetasurfaces can provide spectral tunability by using simpleelectromechanical actuation architectures that allow for such motion.Thereby, an array of independently tunable narrowband infrared filterscan be fabricated that only requires deep-subwavelength motions ofperturbing objects in the resonator's near-field.

The narrowband tunable filter arrays of the present invention are basedupon the Fano metasurfaces described above. In these metasurfaces, asymmetry breaking perturbation of the resonator structure introduces aweak coupling between an incident wave and an extremely high Q-factormagnetic dipole mode. This mode is completely uncoupled from externalradiation in the unperturbed symmetric resonator. The weak couplingresults in the appearance of sharp Fano resonances in the transmissionand reflection spectra of metasurface arrays. For example, consider theFano resonator design based upon germanium shown in FIG. 2. Thesimulated transmission spectrum of the metasurface array, shown in FIG.3, exhibits extremely narrow transmission resonances in the thermal IR(and complementary reflection notches) with Q-factors in excess of 1000.The magnitude and width of the passband can be adjusted by changing thestrength of the symmetry breaking. The inset of FIG. 3 shows theelectric field pattern at the mid-plane of the resonator exhibits acirculating behavior that is characteristic of a z-directed magneticdipole. This Fano metasurface design is scalable from near-IR tomicrowave wavelengths and can be implemented using other highpermittivity materials. As described above, exemplary Fano metasurfacesbased on Si resonators and GaAs resonators have been fabricated thatoperate in the near-IR.

The resonator shown in FIG. 2 uses a cut corner as the source of thesymmetry breaking. However, symmetry breaking can also be introduced byperturbing objects that don't physically touch the resonator, but ratherare placed in the resonator's near-field (e.g., hundreds of nanometers).FIGS. 10A and 10B show the results of full-wave electromagneticsimulations of a symmetric resonator that has a small “perturbing block”located in a symmetry breaking position in the near-field. As with themonolithic resonator of FIG. 2, a sharp Fano resonance appears in thetransmission spectrum. Increasing the gap between the perturbing blockand the cube causes a continuous shifting of the Fano resonance (termed“normal tuning”). In the example shown in FIG. 10A, a small 300 nmmovement of the block normal to the resonator causes the Fano resonanceto shift by many multiples of its linewidth from the zero gap position.A second example of on/off resonance tuning is shown in FIG. 10B. Inthis case, the perturbing block is first placed in a high symmetryposition along the centerline of the resonator. In this example, no Fanoresonance is observed (“centered” curve) when the block is in thecenterline position. Moving the perturbing block laterally, to a lowersymmetry position, results in the appearance of the Fano transmissionresonance (“offset” curve). The spectral location of the Fano resonancewill also tune as the lateral displacement is varied (termed “lateraltuning”). Numerical simulations have also shown that tuning can beachieved through vertical motion of the perturbing block (verticaltuning). These examples show that the required symmetry breaking can beachieved in a variety of ways, including combinations of normal,vertical, and lateral tuning. In principle, the resonator can be anysymmetric structure, such as a cube, sphere, a prism, a pyramid, or acylinder, and the perturbation can be any movable object, such as astraight, tilted, or stepped dielectric block, metallic decoration,liquid droplet, etc. Preferably, the design provides large tuning of thetransmission band, while still maintaining small overall displacementsof the perturbing block.

A MEMS-like electrostatic actuator can be used to achieve the desiredmotion of the perturbing block. FIGS. 11A and 11B show schematicillustrations of an exemplary device for achieving vertical motion ofthe perturbing block. FIG. 11A shows a tunable array 10 in which theperturbing blocks are in unactuated positions relative to the cubicdielectric resonators. Each block 12 is in the near-field on an adjacentdielectric resonator 11. FIG. 11B shows an array 10′ in which theperturbing blocks 12 are in actuated positions relative to the cubicresonators 11. Each block 12 has been moved normally and vertically withrespect to the adjacent dielectric resonator 11 by a cantilever-typeactuator arm 13, which will result in a shift in the Fano resonance. Theactuator arm 13 can be driven, for example, by an electrostaticactuator.

FIGS. 12A and 12B show schematic illustrations of an exemplary devicefor achieving lateral motion of the perturbing block. FIG. 12A shows atunable array 20 in which the perturbing blocks 22 are in a symmetric,unactuated positions relative to the cubic dielectric resonators 21.Each block 22 is in the near-field of an adjacent dielectric resonator21. FIG. 11B shows an array 20′ in which lateral tuning is achieved bycollectively moving all the perturbing blocks 22 laterally with respectto the cubic dielectric resonators 21 with an actuator arm 23. Theactuator arm 23 can be driven, for example, with a comb-drive actuator.

FIGS. 13A and 13B show side-view schematic illustrations of tworesonators of an exemplary tunable array that can be fabricated usingsurface and bulk silicon micromachining. In order to avoid issues withstiction, the perturbing block 32 moves out of the near field of thedielectric resonator 31 when actuated, rather than moving into the nearfield and risking contact. To fabricate the array 30, alternatingground/supply polysilicon traces 34, 35 can be deposited on a siliconnitride-coated silicon wafer 37. The silicon nitride 36 serves as anintermediate and routing layer to affect electrostatic tuning. Apolysilicon stub 38 contacts to the supply traces 35, upon which thepolysilicon resonator 31 can be built up. A perturbing polysilicon block32 can be formed in the same layer as the polysilicon resonators 31, butpositioned over the ground trace 34 without a stub connection. Afterbackfill with sacrificial oxide, thin, conductive polysilicon tethers 33can be deposited, each forming a flexible cantilever arm that alsoelectrically connects a neighboring resonator with the perturbing block32. After patterning the tethers, the sacrificial oxide can be removedwith hydrofluoric acid. An actuator can be provided to move the blockrelative to the resonator (or vice versa). For example, the actuator canconveniently be a simple electrostatic actuator (as shown), althoughother types of micro actuators (e.g., comb drive, magnetic, thermal,piezoelectric, shape memory, or pneumatic actuator) can also be used. Asshown in FIG. 12A, the perturbing block 32 is initially in the nearfield of the adjacent resonator 31. By applying a voltage between therouting layer traces 35 at the periphery of the array, an electrostaticpotential can be formed between the perturbing block 32 and the groundtrace 34, causing the block 32 to deflect downward, as shown in FIG.12B, destroying the asymmetry of the resonator, and hence the Fanoresonance. Note that the block 32 need not actually contact the groundtrace 34.

The present invention has been described as a rapidly tunable,narrow-band infrared filter array. It will be understood that the abovedescription is merely illustrative of the applications of the principlesof the present invention, the scope of which is to be determined by theclaims viewed in light of the specification. Other variants andmodifications of the invention will be apparent to those of skill in theart.

We claim:
 1. A tunable filter array, comprising: a Fano metasurface,comprising: a periodic two-dimensional array of dielectric resonators ona dielectric substrate, and a perturbing object within the near field ofeach dielectric resonator, wherein each dielectric resonator has anelectric or magnetic dipole moment in the plane of the dielectricsubstrate that couples to normally incident light and wherein theperturbing object induces coupling of at least one out-of-plane electricor magnetic dipole moment in the near-field to the in-plane electric ormagnetic dipole moment, whereby the out-of-plane electric or magneticdipole moment provides a narrow spectral resonance within a broadspectral resonance provided by the in-plane electric or magnetic dipolemoment; and an actuator for moving each perturbing object relative toeach dielectric resonator, whereby the narrow spectral resonance can betuned by moving the perturbing objects relative to the dielectricresonators.
 2. The tunable filter array of claim 1, wherein thedielectric resonators comprise germanium, tellurium, silicon, or a IV-VIcompound comprising lead.
 3. The tunable filter array of claim 1,wherein the dielectric resonators comprise a III-IV compound.
 4. Thetunable filter array of claim 3, wherein the III-V compound comprisesgallium arsenide or gallium nitride.
 5. The tunable filter array ofclaim 1, wherein the dielectric substrate comprises a material having alower permittivity than the permittivity of the dielectric resonators.6. The tunable filter array of claim 5, wherein the dielectricresonators comprise Ge and dielectric substrate comprises BaF_(2.) 7.The tunable filter array of claim 1, wherein the dielectric substratefurther comprises an intermediate layer having a lower permittivity thanthe permittivity of the dielectric resonator.
 8. The tunable filterarray of claim 7, wherein the dielectric resonators comprise silicon andthe intermediate layer comprises silicon nitride.
 9. The tunable filterarray of claim 7, wherein the dielectric resonators comprise GaAs andthe intermediate layer comprises AlGaO.
 10. The tunable filter array ofclaim 1, wherein the incident light has a wavelength between 0.75 μm and1 m.
 11. The tunable filter array of claim 10, wherein the incidentlight has a wavelength between 8 μm and 12 μm.
 12. The tunable filterarray of claim 11, wherein the tunability of the narrow spectralresonance is up to 1 μm.
 13. The tunable filter array of claim 1,wherein the narrow spectral resonance has a Q-factor of greater than100.
 14. The tunable filter array of claim 1, wherein the dielectricresonators comprise a cube.
 15. The tunable filter array of claim 1,wherein the dielectric resonators comprise a sphere, a prism, a pyramid,or a cylinder.
 16. The tunable filter array of claim 1, wherein theperturbing object comprises a block.
 17. The tunable filter array ofclaim 16, wherein each block is moved normally with respect to eachdielectric resonator.
 18. The tunable filter array of claim 16, whereineach block is moved laterally with respect to each dielectric resonator.19. The tunable filter array of claim 16, wherein each block is movedvertically with respect to each dielectric resonator.
 20. The tunablefilter array of claim 1, wherein the size of each dielectric resonatoris subwavelength to the incident light.
 21. The tunable filter array ofclaim 1, wherein the size of the periodic two-dimensional array isgreater than a 5×5 array.